Search Results (65)

Pine nuts hold significant economic value due to their rich plant protein and healthy fats, yet precise variety classification has long been hindered by limitations of traditional techniques such as chemical analysis and machine vision. This study proposes a novel near-infrared (NIR) spectral feature selection algorithm, termed the improved binary equilibrium optimizer with selection probability (IBiEO-SP), which incorporates a dynamic probability adjustment mechanism to achieve efficient feature dimensionality reduction. Experimental validation on a dataset comprising seven pine nut varieties demonstrated that, compared to particle swarm optimization (PSO) and the genetic algorithm (GA), the IBiEO-SP algorithm improved average classification accuracy by 5.7% (p < 0.01, Student’s t-test) under four spectral preprocessing methods (MSC, SNV, SG1, and SG2). Remarkably, only 2–3 features were required to achieve optimal performance (MSC + random forest: 99.05% accuracy, 100% F1/precision; SNV + KNN: 97.14% accuracy, 100% F1/precision). Furthermore, a multimodal data synergy strategy integrating NIR spectroscopy with morphological features was proposed, and a classification model was constructed using a soft voting ensemble. The final classification accuracy reached 99.95%, representing a 2.9% improvement over single-spectral-mode analysis. The results indicate that the IBiEO-SP algorithm effectively balances feature discriminative power and model generalization needs, overcoming the contradiction between high-dimensional data redundancy and low-dimensional information loss. This work provides a high-precision, low-complexity solution for rapid quality detection of pine nuts, with broad implications for agricultural product inspection and food safety. Full article

Aiming at the issues of population diversity attenuation, insufficient search efficiency, and susceptibility to a local optimum in the equilibrium optimizer (EO), a dynamic heterogeneous search-mutation structure-based equilibrium optimizer (DHSMEO) is developed. First of all, a dynamic dual-subpopulation adaptive grouping strategy is constructed to boost population diversity, and it provides an effective information-exchange structure for the heterogeneous hybrid search strategy. Then, a heterogeneous hybrid search-based concentration-updating strategy is integrated to enhance search efficiency. Finally, a dynamic Levy mutation-based optimal equilibrium candidate-refining strategy is incorporated to strengthen the capability of escaping local optima. The optimization capability of DHSMEO is evaluated using 39 typical benchmark functions, and the experimental results validate its effectiveness and superiority. Moreover, the practicality of DHSMEO in solving the practical optimization problem is validated through the UAV mountain path planning problem. Full article

To strengthen the population diversity and search capability of equilibrium optimizer (EO), a dynamic multi-population mutation architecture-based equilibrium optimizer (DMMAEO) is proposed. Firstly, a dynamic multi-population guidance mechanism is constructed to enhance population diversity. Secondly, a dynamic Gaussian mutation-based sub-population concentration updating mechanism is introduced to strengthen exploitation ability. Finally, a dynamic Cauchy mutation-based sub-population equilibrium candidate generation mechanism is integrated to boost exploration ability. The optimization ability of DMMAEO is assessed through a comparison with several recent promising algorithms on 58 test functions (including 29 representative test functions and 29 CEC2017 test functions). The comparison results reveal that the DMMAEO has superiority in the performance assessment of seeking global optimum over other compared algorithms. The DMMAEO is further employed in addressing six engineering design problems and a UGV multi-target path planning problem. The results show the practicality of DMMAEO in addressing engineering application tasks. The aforementioned numerical optimization and engineering application experimental results show that the three enhancement mechanisms of DMMAEO improve the optimization ability of the canonical EO, and the DMMAEO has competitiveness in tackling various kinds of complex numerical optimization and engineering application problems. Full article

Numerous optimization problems exist in the design and operation of power systems, critical for efficient energy use, cost minimization, and system stability. With increasing energy demand and diversifying energy structures, these problems grow increasingly complex. Metaheuristic algorithms have been highlighted for their flexibility and effectiveness in addressing such complex problems. To further explore the theoretical support of metaheuristic algorithms for optimization problems in power systems, this paper proposes a novel algorithm, the Boston Consulting Group Matrix-based Equilibrium Optimizer (BCGEO), which integrates the Equilibrium Optimizer (EO) with the classic economic decision-making model, the Boston Consulting Group Matrix. This matrix is utilized to construct a model for evaluating the potential of individuals, aiding in the rational allocation of computational resources, thereby achieving a better balance between exploration and exploitation. In comparative experiments across various dimensions on CEC2017, the BCGEO demonstrated superior search performance over its peers. Furthermore, in dynamic economic dispatch, the BCGEO has shown strong optimization capabilities and potential in power system optimization problems. Additionally, the experimental results in the spacecraft trajectory optimization problem suggest its potential for broader application across various fields. Full article

Steam reforming is an important industrial process for hydrogen production. Acetone, the by-product of phenol production from cumene peroxidation, is a useful source of hydrogen due to its availability and low value compared to hydrogen fuel. This study aimed to utilize the Gibbs free energy minimization method using the Soave–Redlich–Kwong (SRK) equation of state (EOS) to conduct a thermodynamic analysis of the steam reforming process for pure component acetone. The steam reforming process is temperature dependent, with increasing temperatures leading to higher hydrogen production. Competing reactions, particularly the exothermic reverse water–gas shift, impact hydrogen yields beyond 650 °C. The study identified 600 °C as the optimum temperature to strike a balance between maximizing hydrogen production and minimizing the reverse water–gas shift’s impact. The optimal hydrogen yield (70 mol%) was achieved at a steam-to-oil ratio (STOR) of 12. High STOR values shift the equilibrium of the water–gas shift reaction towards hydrogen production due to increased steam, effectively consuming acetone and favoring the desired product. Atmospheric pressure is optimum for hydrogen production because the equilibrium of gas phase reactions shifts in favor of the lighter components at lower pressures. Full article

The study applies the black kite algorithm (BKA), equilibrium optimizer (EO), and secretary bird optimization algorithm (SBOA) to optimize the placement of electric vehicle charge stations (EVCSs), wind turbine stations (WTSs), photovoltaic units (PVUs), and capacitor banks (CAPBs) in the IEEE 69-node distribution power grid. Three single objectives, including power loss minimization, grid power minimization, and total voltage deviation improvement, are considered. For each objective function, five scenarios are simulated under one single operation hour, including (1) place-only EVCSs; (2) place EVCSs and PVUs; (3) place EVCSs, PVUs, and CAPBs; (4) EVCSs and WTSs; and (5) EVCSs, PVUs, WTSs, and CAPBs. The results indicate that the EO can find the best solutions for the five scenarios. The results indicate that the EO and SBOA are the two powerful algorithms that can find optimal solutions for simulation cases. For one operating day, the total grid energy that is supplied to base loads and charge stations is 80,153.1 kWh, and many nodes at high load factors violate the lower limit of 0.95 pu. As for installing more renewable power sources, the energy that the base loads and charge stations need to supply from the grid is 39,713.4 kWh. As more capacitor banks are installed, the energy demand continues to be reduced to 39,578.9 kWh. The energy reduction is greater than 50% of the demand of all base loads and charge stations. Furthermore, the voltage can be significantly improved up to higher than 0.95 pu, and a few nodes at a few hours fall into the lowest range. Thus, the study concludes that the economic and technical aspects can be guaranteed for DPGs with additional installation of EVCSs. Full article

The Equilibrium Optimizer (EO) is an optimization algorithm inspired by a physical law called mass balance, which represents the amount of mass entering, leaving, and being produced in a control volume. Although the EO is a well-accepted and successful algorithm in the literature, it needs improvements in the search, exploration, and exploitation phases. Its main problems include low convergence, getting stuck in local minima, and imbalance between the exploration and exploitation phases. This paper introduces the Boosted Equilibrium Optimizer (BEO) algorithm, where improvements are proposed to solve these problems and improve the performance of the EO algorithm. New methods are proposed for the three important phases of the algorithm: initial population, candidate pool generation, and updating. In the proposed algorithm, the exploration phase is strengthened by using a uniformly distributed random initial population instead of the traditional random initial population and a versatile concentration pool strategy. Furthermore, the balance between the exploration and exploitation phases is improved with two new approaches proposed for the updating phase. These novel methods enhance the algorithm’s performance by more effectively balancing exploration and exploitation. The proposed algorithm is tested using a total of 23 standard test functions, including unimodal, multimodal, and fixed-size multimodal. The results are supported by numerical values and graphs. In addition, the proposed BEO algorithm is applied to solve real-world engineering design problems. The BEO outperforms the original EO algorithm on all problems. Full article

With the continuous exploitation of offshore natural gas, the content of CO₂ produced gradually increases. It is not economical to separate more CO₂ from natural gas after transportation, and more CO₂ will aggravate the corrosion of pipelines. The commonly used decarburization process is not suitable for offshore platforms, and there are problems of high energy consumption and large space occupation. Therefore, dense phase separation of associated gas with high carbon dioxide content is a better separation method. In this paper, the equation of state is optimized by comparing the experimental and CO₂ system phase characteristics simulation. Based on the selected equation of state (EOS), a three-level separation model of phase equilibrium characteristics is established. The separation efficiency is simulated to complete the separation of CO₂ and methane. The separation process is optimized by a genetic algorithm, and the temperature and pressure under the best separation efficiency are determined. The PR-EOS was selected as the equation with the highest calculation accuracy. Through process simulation and algorithm optimization, the best separation efficiency was 72.23%. Full article

This paper examines the effectiveness of a pumped storage hydropower plant (PSHP) when combined with other plants. System 1 examines the contribution of the PSHP to reducing fuel costs for thermal power plants. System 2 examines the optimization of operations for power systems with energy storage and uncertain renewable energies to maximize total profit based on four test system cases: Case 1: neglect the PSHP and consider wind and solar certainty; Case 2: consider the PSHP and wind and solar certainty; Case 3: neglect the PSHP and consider wind and solar uncertainty; and Case 4: consider the PSHP and wind and solar uncertainty. Cases 1 and 2 focus on systems that assume stable power outputs from these renewable energy sources, while Cases 3 and 4 consider the uncertainty surrounding their power output. The presence of a PSHP has a key role in maximizing the system’s total profit. This proves that Case 2, which incorporates a PSHP, achieves a higher total profit than Case 1, which does not include a PSHP. The difference is USD 17,248.60, representing approximately 0.35% for a single day of operation. The total profits for Cases 3 and 4 are USD 5,089,976 and USD 5,100,193.80, respectively. Case 4 surpasses Case 3 by USD 10,217.70, which is about 0.2% of Case 3’s total profit. In particular, the PSHP used in Cases 2 and 4 is a dispatching tool that aims to achieve the highest profit corresponding to the load condition. The PSHP executes its storage function by using low-price electricity at off-peak periods to store water in the reservoir through the pumping mode and discharge water downstream to produce electricity at periods with high electricity prices using the generating mode. As a result, the total profit increases. A modified slime mould algorithm (MSMA) is applied to System 2 after proving its outstanding performance compared to the jellyfish search algorithm (JS), equilibrium optimizer (EO), and slime mould algorithm (SMA) in System 1. Full article

This research paper focuses on the application of a new method for the simultaneous reconfiguration and the optimum placing of Soft Open Points (SOPs) in Radial Distribution Systems (RDS). The proposed Lévy Flight-based Improved Equilibrium Optimizer (LF-IEO) algorithm enhances the standard Equilibrium Optimizer (EO) by integrating several techniques to improve exploration and exploitation capabilities. SOPs are highly developed power electronics devices that can enhance distribution utility networks in terms of reliability and effectiveness. However, identifying their optimum place along with network reconfiguration is a challenging task that requires advanced computation techniques. The performance of the proposed LF-IEO algorithm has been first verified on several benchmark functions. Subsequently, it is implemented on a IEEE 33-Bus, 69-Bus, 118-Bus, and Algerian 116-Bus distribution network to solve the problem of simultaneous network reconfiguration and optimal SOP placement. For the Algerian 116-bus system case study, the algorithm achieved a significant 14.89% reduction in power losses, improved the minimum voltage, and generated substantial net annual savings of 74,426.40 $/year. To prove its superiority in terms of solution quality and robustness, the proposed LF-IEO approach was compared with several newly developed algorithms from the literature. Full article

Industrial Control Systems (ICSs) are vital components of industrial production, and their security posture significantly impacts operational safety. Given that ICSs frequently interact with external networks, cyberattacks can disrupt system symmetry, thereby affecting industrial processes. This paper aims to predict the network security posture of ICSs to ensure system symmetry. A prediction model for the network security posture of ICSs was established utilizing Evidence Reasoning (ER) and Explainable Belief Rule Base (BRB-e) technologies. Initially, an evaluation framework for the ICS architecture was constructed, integrating data from various layers using ER. The development of the BRB prediction model requires input from domain experts to set initial parameters; however, the subjective nature of these settings may reduce prediction accuracy. To address this issue, an ICS network security posture prediction model based on the Explainable Belief Rule Base (BRB-e) was proposed. The modeling criteria for explainability were defined based on the characteristics of the ICS network, followed by the design of the inference process for the BRB-e prediction model to enhance accuracy and precision. Additionally, a parameter optimization method for the explainable BRB-e prediction model is presented using a constrained Projection Equilibrium Optimization (P-EO) algorithm. Experiments utilizing industrial datasets were conducted to validate the reliability and effectiveness of the prediction model. Comparative analyses indicated that the BRB-e model demonstrates distinct advantages in both prediction accuracy and explainability when compared to other algorithms. Full article

Over the past decade, the development of computer-aided detection tools for medical image analysis has seen significant advancements. However, tasks such as the automatic differentiation of tissues or regions in medical images remain challenging. Magnetic resonance imaging (MRI) has proven valuable for early diagnosis, particularly in conditions like prostate cancer, yet it often struggles to produce high-resolution images with clearly defined boundaries. In this article, we propose a novel segmentation approach based on minimum cross-entropy thresholding using the equilibrium optimizer (MCE-EO) to enhance the visual differentiation of tissues in prostate MRI scans. To validate our method, we conducted two experiments. The first evaluated the overall performance of MCE-EO using standard grayscale benchmark images, while the second focused on a set of transaxial-cut prostate MRI scans. MCE-EO’s performance was compared against six stochastic optimization techniques. Statistical analysis of the results demonstrates that MCE-EO offers superior performance for prostate MRI segmentation, providing a more effective tool for distinguishing between various tissue types. Full article

The study maximizes the total profit of a hybrid power system with cascaded hydropower plants, thermal power plants, pumped storage hydropower plants, and wind and solar power plants over one operation day, considering the uncertainty of wind speed and solar radiation. Wind speed and solar radiation in a specific zone in Vietnam are collected using the wind and solar global atlases, and the maximum data are then supposed to be 120% of the collection for uncertainty consideration. The metaheuristic algorithms, including the original Slime mould algorithm (SMA), Equilibrium optimizer, and improved Slime mould algorithm (ISMA), are implemented for the system. ISMA is a developed version of SMA that cancels old methods and proposes new methods of updating new solutions. In the first stage, the cascaded system with four hydropower plants is optimally operated by simulating two cases: simultaneous optimization and individual optimization. ISMA is better than EO and SMA for the two cases, and the results of ISMA from the simultaneous optimization reach greater energy than individual optimization by 154.8 MW, equivalent to 4.11% of the individual optimization. For the whole system, ISMA can reach a greater total profit than EO and SMA over one operating day by USD 6007.5 and USD 650.5, equivalent to 0.12% and 0.013%. The results indicate that the optimization operation of cascaded hydropower plants and hybrid power systems can reach a huge benefit in electricity sales Full article

This study focused on the efficacy of employing a pulsed fiber laser in the curved cutting of thin, non-oriented electrical steel sheets. Experiments were conducted in paraffinic oil by adjusting the input process parameters, including laser power, pulse frequency, cutting speed, and curvature radius. The multiple output quality metrics included kerf width, inner and outer heat-affected zones, and re-welded portions. Analyses of the Random Forest Method and Response Surface Method indicated that laser pulse frequency was the most important variable affecting the cut quality, followed by laser power, curvature radius, and cutting speed. To improve cut quality, an innovative artificial intelligence (AI) approach incorporating a deep neural network (DNN) model and a modified equilibrium optimizer (M-EO) was proposed. Initially, the DNN model established correlations between input parameters and cut quality aspects, followed by M-EO pinpointing optimal cut qualities. Such an approach successfully identified an optimal set of laser process parameters, even beyond the specified process window from the initial experiments on curved cuts, resulting in significant enhancements confirmed by validation experiments. A comparative analysis showcased the developed models’ superior performance over prior studies. Notably, while the models were initially developed based on the results from curved cuts, they proved adaptable and capable of yielding comparable outcomes for straight cuts as well. Full article

The Location-Routing Problem (LRP) becomes a more intricate subject when the limits of capacities of vehicles and warehouses are considered, which is an NP-hard problem. Moreover, as the number of vehicles increases, the solution to LRP is exacerbated because of the complexity of transportation and the combination of routes. To solve the problem, this paper proposed a Discrete Assembly Combination-Delivery (DACA) strategy based on, the Binary Equilibrium Optimizer (BiEO) algorithm, in addition, this paper also proposes a mixed-integer linear programming model for the problem of this paper. Our primary objective is to address both the route optimization problem and the assembly group sum problem concurrently. Our BiEO algorithm was designed as discrete in decision space to meet the requirements of the LRP represented by the DACA strategy catering to the multi-vehicle LRP scenario. The efficacy of the BiEO algorithm with the DACA strategy is demonstrated. through empirical analysis utilizing authentic data from Changchun City, China, Remarkably, the experiments reveal that the BiEO algorithm outperforms conventional methods, specifically GA, PSO, and DE algorithms, resulting in reduced costs. Notably, the results show the DACA strategy enables the simultaneous optimization of the LRP and the vehicle routing problem (VRP), ultimately leading to cost reduction. This innovative algorithm proficiently tackles both the assembly group sum and route optimization problems intrinsic to multi-level LRP instances. Full article